There is a risk that Liam Byrne is destined to be remembered, if at all, as the author of the dumbest joke in British political history. In May 2010, a gloating David Laws revealed that Byrne, his immediate predecessor as chief secretary to the Treasury, had left a note on his way out, saying: "There's no money left." Byrne had assumed his hilarious message would be picked up and treated discreetly by his Tory counterpart, Philip Hammond, with whom he had a rapport. He hadn't bargained on coalition. But the joke served as a framing device for the new government's narrative: the cause of the deficit was not a global economic crash but Labour's fiscal incontinence. Even their very own chief secretary had admitted as much.

Now Byrne has a chance to write himself a different place in the annals – as the pivotal figure in a new and welcome shift in our nation's politics. For Byrne has announced that if the voters of Birmingham opt on 3 May to create a directly elected mayoralty, he will quit his post in the shadow cabinet and his seat in parliament to stand for the job. There is no clearer indication of politicians' true priorities than what they choose to do with their own careers. By this move, and the risk it entails, Byrne is declaring that sometimes local trumps national.

He won't be the first. Besides Ken Livingstone and Boris Johnson – whose conduct this week, admittedly, has been no advert for urban democracy – there are other, albeit less ballyhooed, examples of politicians trading the central for the municipal. One of Byrne's rivals for the Labour mayoral candidacy in Birmingham is Siôn Simon, a Commons colleague until 2010. Another is Gisela Stuart, who clung on to her Edgbaston seat that year against every prediction. Not far away sits former MP Peter Soulsby, now installed as mayor of Leicester. Expect a raft of similar moves if Bradford, Bristol, Coventry, Leeds, Manchester, Newcastle, Nottingham, Sheffield and Wakefield vote on 3 May to join Liverpool and Salford in having mayors of their own. Meanwhile, in Hull, a former deputy prime minister, no less, seeks to become police commissioner.

A jaundiced eye would see Byrne and the others as rats abandoning a plunging ship: look, they've given up on Ed Miliband leading them to victory and are grabbing hold of whatever small slice of power they can seize instead. Such an interpretation is easy but itself a symptom of Britain's long-running political disease. The cognoscenti have long disparaged local government, disdaining it as at best a mere stepping stone to Westminster, rather than a democratic space in its own right. That attitude will be on show again next month, when local election results are read simply as a glorified opinion poll on the state of the parties in Westminster.

Such thinking looks increasingly out of date. Take Byrne's move. His friends say he wants the job because he enjoys government more than he enjoys politics, that he is not "built for opposition". If governing is what he likes, you can see why the Birmingham job appeals. The mayor will be in charge of a £2bn budget, with executive clout few cabinet ministers can match. He or she will be responsible for everything from social services to schools, local planning to street lighting, with a big say over fire services and transport. The new mayor will have greater power over Birmingham than Boris and Ken have ever wielded in London, with no pesky boroughs to share authority. According to the pre-eminent scholar of local government, Tony Travers: "There will be more power in the hands of the mayor of Birmingham than any civic leader of modern times."

All that is clearly good news for the city that still remembers the municipal glory days of the late Victorian era, when Britain's cities governed themselves and deployed serious political muscle, when a Joseph Chamberlain could transform Birmingham, given his head by an imperial parliament in Westminster more concerned with ruling Canada and India than providing running water in Dudley or trams to West Bromwich. Birmingham has not forgotten that past: the local political blog is called The Chamberlain Files.

Joseph's would-be 21st-century heirs promise to be ambassadors and cheerleaders for their city, perhaps even offering tax breaks – a reduced business rate, say – to lure investment and jobs. That would obviously benefit Birmingham but it would also help Britain. Few deny that our country's extreme dominance by London has distorted much of our national life, cultural and especially economic: the lopsided tilt towards finance over industry is partly a function of the capital's excessive might. If mayors help the other cities catch up, that can only be good.

Labour has a particular stake in this return to the local. One party strategist sees the creation of a dozen big city mayoralties as a chance for Labour to prove its fitness to govern in time for 2015. "If we show that we can lead these big cities with big problems, that we are not wasteful, that we are not all heart and no muscle then this will be the best possible showcase." Sure, such thinking betrays that old view of town hall as Westminster nursery slope, but it's powerful all the same.

And yet Labour should take nothing for granted. For the lesson of George Galloway's victory in Bradford West – that in today's volatile climate voters are ready to back mavericks, so long as they articulate their very specific concerns – surely applies even more to direct, highly personalised mayoral contests than to parliamentary ones. If I were Byrne, Simon or Stuart, I would be eyeing rather nervously Respect's latest hint that it might put up a candidate in Birmingham.

So there are dangers for Labour seeking mayoralties in cities it has long regarded as home turf. Labour is the establishment in many of them, ripe for a Bradford-style kicking. Party leaders will need to be on their mettle. That's one reason why Labour's national executive must not repeat in Birmingham the experience of London, offering members too narrow a choice of candidates: it should let all three hopefuls on to the ballot, rather than presenting the rumoured shortlist of two, with only one of Byrne or Simon allowed to go through.

So, yes, there are dangers, but there is also opportunity – the best chance of power Labour will have this side of 2015. The party mustn't blow it.